CURCY Using a fixed price currency but with a variable checkout currency?

Can prices be set in ONE fixed currency but all other currencies are variable including a fixed checkout currency?

Running a shop in an unusual country would make it useful to run the shop in one of the leading currencies though like USD, EUR, GBP.

If it was just ONE price setting currency and ONE checkout currency it might be easy but offering customers the convenience of converting the price setting currency (e.g. EUR) into their own one (out of like 10 available) but finally the checkout currency is being used (AED) which is always adjusted using exchange rates.
So actually the price in the checkout currency will be variable depending on the product price in another currency.